TY - JFULL
AU - Feng Cheng Chang
PY - 2008/12/
TI - Factoring a Polynomial with Multiple-Roots
T2 - International Journal of Computer and Information Engineering
SP - 3717
EP - 3721
VL - 2
SN - 1307-6892
UR - https://publications.waset.org/pdf/10086
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 23, 2008
N2 - A given polynomial, possibly with multiple roots, is
factored into several lower-degree distinct-root polynomials with
natural-order-integer powers. All the roots, including multiplicities,
of the original polynomial may be obtained by solving these lowerdegree
distinct-root polynomials, instead of the original high-degree
multiple-root polynomial directly.
The approach requires polynomial Greatest Common Divisor
(GCD) computation. The very simple and effective process, “Monic
polynomial subtractions" converted trickily from “Longhand
polynomial divisions" of Euclidean algorithm is employed. It
requires only simple elementary arithmetic operations without any
advanced mathematics.
Amazingly, the derived routine gives the expected results for the
test polynomials of very high degree, such as p( x) =(x+1)1000.
ER -